St Peter is the Rock because he first confessed that Jesus is the Messiah.
That is the rock on which all our faith is built. Yes, St Peter was the father of the Church in Rome and all the Popes, good, bad and indifferent, follow on from him. However, St Peter was also the first Bishop of Antioch, therefore the Patriarch of the Syriac Orthodox Church is equally Peter's descendent.
The quarrel with Rome is that they forget the equality of Bishops (all Bishops are equal, all Eucharists are equal) and stress Rome's primacy.
Orthodoxy argues for this equality and is the only theologically tenable position.